I do a complete deep clean 2-3 times a year, always right before winter (and usually right after, too, because it gets so mucky in the rain/snow). I figure the birds will be stuck inside a lot of the time making it dirtier and less sanitary, so if I clean it out really well before hand, it'll be...
The shower curtains worked well on my old run. We didn't get snow where we lived at the time, but it rained often and we had "wind events."
There are "clear" tarps folks here use to enclose porches. They are pricier than shower curtains, naturally, but tougher by far. I liked the shower...
Before I lived out here in the woods, I used cheap plastic shower curtains on rods I attached to the run's roof. I left one end open (depending on the direction of the rain). Now I have clear corrugated plastic panels I attach with magnetic hooks (my run is a big ol' dog kennel). Works great...